*> \brief \b ZLAGGE * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * * .. Scalar Arguments .. * INTEGER INFO, KL, KU, LDA, M, N * .. * .. Array Arguments .. * INTEGER ISEED( 4 ) * DOUBLE PRECISION D( * ) * COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZLAGGE generates a complex general m by n matrix A, by pre- and post- *> multiplying a real diagonal matrix D with random unitary matrices: *> A = U*D*V. The lower and upper bandwidths may then be reduced to *> kl and ku by additional unitary transformations. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] KL *> \verbatim *> KL is INTEGER *> The number of nonzero subdiagonals within the band of A. *> 0 <= KL <= M-1. *> \endverbatim *> *> \param[in] KU *> \verbatim *> KU is INTEGER *> The number of nonzero superdiagonals within the band of A. *> 0 <= KU <= N-1. *> \endverbatim *> *> \param[in] D *> \verbatim *> D is DOUBLE PRECISION array, dimension (min(M,N)) *> The diagonal elements of the diagonal matrix D. *> \endverbatim *> *> \param[out] A *> \verbatim *> A is COMPLEX*16 array, dimension (LDA,N) *> The generated m by n matrix A. *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the array A. LDA >= M. *> \endverbatim *> *> \param[in,out] ISEED *> \verbatim *> ISEED is INTEGER array, dimension (4) *> On entry, the seed of the random number generator; the array *> elements must be between 0 and 4095, and ISEED(4) must be *> odd. *> On exit, the seed is updated. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (M+N) *> \endverbatim *> *> \param[out] INFO *> \verbatim *> INFO is INTEGER *> = 0: successful exit *> < 0: if INFO = -i, the i-th argument had an illegal value *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \date November 2015 * *> \ingroup complex16_matgen * * ===================================================================== SUBROUTINE ZLAGGE( M, N, KL, KU, D, A, LDA, ISEED, WORK, INFO ) * * -- LAPACK auxiliary routine (version 3.6.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2015 * * .. Scalar Arguments .. INTEGER INFO, KL, KU, LDA, M, N * .. * .. Array Arguments .. INTEGER ISEED( 4 ) DOUBLE PRECISION D( * ) COMPLEX*16 A( LDA, * ), WORK( * ) * .. * * ===================================================================== * * .. Parameters .. COMPLEX*16 ZERO, ONE PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ), $ ONE = ( 1.0D+0, 0.0D+0 ) ) * .. * .. Local Scalars .. INTEGER I, J DOUBLE PRECISION WN COMPLEX*16 TAU, WA, WB * .. * .. External Subroutines .. EXTERNAL XERBLA, ZGEMV, ZGERC, ZLACGV, ZLARNV, ZSCAL * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN * .. * .. External Functions .. DOUBLE PRECISION DZNRM2 EXTERNAL DZNRM2 * .. * .. Executable Statements .. * * Test the input arguments * INFO = 0 IF( M.LT.0 ) THEN INFO = -1 ELSE IF( N.LT.0 ) THEN INFO = -2 ELSE IF( KL.LT.0 .OR. KL.GT.M-1 ) THEN INFO = -3 ELSE IF( KU.LT.0 .OR. KU.GT.N-1 ) THEN INFO = -4 ELSE IF( LDA.LT.MAX( 1, M ) ) THEN INFO = -7 END IF IF( INFO.LT.0 ) THEN CALL XERBLA( 'ZLAGGE', -INFO ) RETURN END IF * * initialize A to diagonal matrix * DO 20 J = 1, N DO 10 I = 1, M A( I, J ) = ZERO 10 CONTINUE 20 CONTINUE DO 30 I = 1, MIN( M, N ) A( I, I ) = D( I ) 30 CONTINUE * * Quick exit if the user wants a diagonal matrix * IF(( KL .EQ. 0 ).AND.( KU .EQ. 0)) RETURN * * pre- and post-multiply A by random unitary matrices * DO 40 I = MIN( M, N ), 1, -1 IF( I.LT.M ) THEN * * generate random reflection * CALL ZLARNV( 3, ISEED, M-I+1, WORK ) WN = DZNRM2( M-I+1, WORK, 1 ) WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = WORK( 1 ) + WA CALL ZSCAL( M-I, ONE / WB, WORK( 2 ), 1 ) WORK( 1 ) = ONE TAU = DBLE( WB / WA ) END IF * * multiply A(i:m,i:n) by random reflection from the left * CALL ZGEMV( 'Conjugate transpose', M-I+1, N-I+1, ONE, $ A( I, I ), LDA, WORK, 1, ZERO, WORK( M+1 ), 1 ) CALL ZGERC( M-I+1, N-I+1, -TAU, WORK, 1, WORK( M+1 ), 1, $ A( I, I ), LDA ) END IF IF( I.LT.N ) THEN * * generate random reflection * CALL ZLARNV( 3, ISEED, N-I+1, WORK ) WN = DZNRM2( N-I+1, WORK, 1 ) WA = ( WN / ABS( WORK( 1 ) ) )*WORK( 1 ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = WORK( 1 ) + WA CALL ZSCAL( N-I, ONE / WB, WORK( 2 ), 1 ) WORK( 1 ) = ONE TAU = DBLE( WB / WA ) END IF * * multiply A(i:m,i:n) by random reflection from the right * CALL ZGEMV( 'No transpose', M-I+1, N-I+1, ONE, A( I, I ), $ LDA, WORK, 1, ZERO, WORK( N+1 ), 1 ) CALL ZGERC( M-I+1, N-I+1, -TAU, WORK( N+1 ), 1, WORK, 1, $ A( I, I ), LDA ) END IF 40 CONTINUE * * Reduce number of subdiagonals to KL and number of superdiagonals * to KU * DO 70 I = 1, MAX( M-1-KL, N-1-KU ) IF( KL.LE.KU ) THEN * * annihilate subdiagonal elements first (necessary if KL = 0) * IF( I.LE.MIN( M-1-KL, N ) ) THEN * * generate reflection to annihilate A(kl+i+1:m,i) * WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 ) WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( KL+I, I ) + WA CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) A( KL+I, I ) = ONE TAU = DBLE( WB / WA ) END IF * * apply reflection to A(kl+i:m,i+1:n) from the left * CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE, $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, $ WORK, 1 ) CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, $ 1, A( KL+I, I+1 ), LDA ) A( KL+I, I ) = -WA END IF * IF( I.LE.MIN( N-1-KU, M ) ) THEN * * generate reflection to annihilate A(i,ku+i+1:n) * WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA ) WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( I, KU+I ) + WA CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) A( I, KU+I ) = ONE TAU = DBLE( WB / WA ) END IF * * apply reflection to A(i+1:m,ku+i:n) from the right * CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA ) CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE, $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, $ WORK, 1 ) CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), $ LDA, A( I+1, KU+I ), LDA ) A( I, KU+I ) = -WA END IF ELSE * * annihilate superdiagonal elements first (necessary if * KU = 0) * IF( I.LE.MIN( N-1-KU, M ) ) THEN * * generate reflection to annihilate A(i,ku+i+1:n) * WN = DZNRM2( N-KU-I+1, A( I, KU+I ), LDA ) WA = ( WN / ABS( A( I, KU+I ) ) )*A( I, KU+I ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( I, KU+I ) + WA CALL ZSCAL( N-KU-I, ONE / WB, A( I, KU+I+1 ), LDA ) A( I, KU+I ) = ONE TAU = DBLE( WB / WA ) END IF * * apply reflection to A(i+1:m,ku+i:n) from the right * CALL ZLACGV( N-KU-I+1, A( I, KU+I ), LDA ) CALL ZGEMV( 'No transpose', M-I, N-KU-I+1, ONE, $ A( I+1, KU+I ), LDA, A( I, KU+I ), LDA, ZERO, $ WORK, 1 ) CALL ZGERC( M-I, N-KU-I+1, -TAU, WORK, 1, A( I, KU+I ), $ LDA, A( I+1, KU+I ), LDA ) A( I, KU+I ) = -WA END IF * IF( I.LE.MIN( M-1-KL, N ) ) THEN * * generate reflection to annihilate A(kl+i+1:m,i) * WN = DZNRM2( M-KL-I+1, A( KL+I, I ), 1 ) WA = ( WN / ABS( A( KL+I, I ) ) )*A( KL+I, I ) IF( WN.EQ.ZERO ) THEN TAU = ZERO ELSE WB = A( KL+I, I ) + WA CALL ZSCAL( M-KL-I, ONE / WB, A( KL+I+1, I ), 1 ) A( KL+I, I ) = ONE TAU = DBLE( WB / WA ) END IF * * apply reflection to A(kl+i:m,i+1:n) from the left * CALL ZGEMV( 'Conjugate transpose', M-KL-I+1, N-I, ONE, $ A( KL+I, I+1 ), LDA, A( KL+I, I ), 1, ZERO, $ WORK, 1 ) CALL ZGERC( M-KL-I+1, N-I, -TAU, A( KL+I, I ), 1, WORK, $ 1, A( KL+I, I+1 ), LDA ) A( KL+I, I ) = -WA END IF END IF * IF (I .LE. N) THEN DO 50 J = KL + I + 1, M A( J, I ) = ZERO 50 CONTINUE END IF * IF (I .LE. M) THEN DO 60 J = KU + I + 1, N A( I, J ) = ZERO 60 CONTINUE END IF 70 CONTINUE RETURN * * End of ZLAGGE * END